Analytical and Numerical Solutions for Frames with Softening Hinges
Publication: Journal of Engineering Mechanics
Volume 123, Issue 1
Abstract
The paper describes beam elements with inelastic hinges capable of modeling softening due to damage in building frames under severe loadings. A condition for uniqueness on the element level is derived, and the behavior of the model is compared to analytical solutions of simple structures (a single column and a portal frame). An application to postpeak analysis of a multibay frame is presented. Depending on the beam-to-column stiffness ratio and on a certain ductility parameter, various failure modes can occur, ranging from distributed to highly localized ones. This leads to a special type of size effect on the peak load, which is assessed numerically and related to analytically derived solutions valid in extreme situations—the elastic limit and the plastic limit.
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References
1.
Bažant, Z. P. (1976). “Instability, ductility, and size effect in strain-softening concrete.”J. Engrg. Mech., ASCE, 102(2), 331–344; “Closure to,” 103, 357–8 and 775–7.
2.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: elastic, inelastic, fracture and damage theories. Oxford Univ. Press, New York, N.Y.
3.
Bažant, Z. P., and Jirásek, M. (1995). “Seismic localization of softening cracking damage in concrete frames.”Fracture Mechanics of Concrete Structures, Proc., FraMCoS-2, F. H. Wittmann, ed., Aedificatio Publishers, Freiburg, Germany, 1397–1406.
4.
Bažant, Z. P., and Jirásek, M.(1996). “Softening-induced dynamic localization instability: seismic damage in frames.”J. Engrg. Mech., ASCE, 122(12), 1149–1158.
5.
Bažant, Z. P., and Kazemi, M. T. (1994). “Localization of softening damage in frames and implications for earthquake resistance.”Proc., 5th U.S. Nat. Conf. on Earthquake Engrg., Vol. 1, Earthquake Engrg. Res. Inst., Oakland, Calif., 313–322.
6.
Bažant, Z. P., Pan, J.-Y., and Pijaudier-Cabot, G.(1987a). “Softening in reinforced concrete beams and frames.”J. Struct. Engrg., ASCE, 113(12), 2333–2347.
7.
Bažant, Z. P., Pijaudier-Cabot, G., and Pan, J.-Y.(1987b). “Ductility, snapback, size effect, and redistribution in softening beams and frames.”J. Struct. Engrg., ASCE, 113(12), 2348–2364.
8.
Cranston, W. B. (1965). “Tests on reinforced concrete frames. I: Pinned portal frames.”Tech. Rep. TRA/392, Cement and Concrete Assn., London, England.
9.
Darvall, P. L.(1984). “Critical softening of hinges in portal frames.”J. Struct. Engrg., ASCE, 110(1), 157–162.
10.
Hunt, G. W., and Baker, G.(1995). “Principles of localization in the fracture of quasi-brittle structure.”J. Mech. and Phys. of Solids, 43, 1127–1150.
11.
Maier, G., and Zavelani, A.(1970). “Sul comportamento di aste metalliche compresse eccentricamente. Indagine sperimentale e considerazioni teoriche.”Costruzioni Metalliche, 22(4), 282–297.
12.
Maier, G. (1971). “Instability due to strain softening.”Stability of Continuous Systems, Proc., IUTAM Symp., Springer-Verlag, KG, Berlin, 411–417.
13.
Maier, G., Zavelani, A., and Dotreppe, J. C.(1973). “Equilibrium branching due to flexural softening.”J. Engrg. Mech., ASCE, 99(4), 897–901.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Jan 1, 1997
Published in print: Jan 1997
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